Multiple-qubit wave-activated controlled gate

ABSTRACT

A device includes a housing, at least two qubits disposed in the housing and a resonator disposed in the housing and coupled to the at least two qubits, wherein the at least two qubits are maintained at a fixed frequency and are statically coupled to one another via the resonator, wherein energy levels |03&gt; and |12&gt; are closely aligned, wherein a tuned microwave signal applied to the qubit activates a two-qubit phase interaction.

FEDERAL RESEARCH STATEMENT

This invention was made with Government support under Contract No.:W911NF-10-1-0324 awarded by the U.S. Army. The Government has certainrights in this invention.

BACKGROUND

The present invention relates to quantum computing, and morespecifically, to systems and methods for a two-qubit microwave-activatedcontrolled phase gate.

Superconducting qubits have made considerable progress recently inexperimental controls for generating a universal set of quantum gatesfor quantum computing. Analogous to how classical algorithms can bebuilt from a universal logic gate, such as a NAND gate, all quantumalgorithms can be constructed from a universal set of quantum gates. Ithas theoretically been proven that such a universal set includesarbitrary single qubit rotation gates and a two-qubit entangling gate.The quality of these gates are characterized by a metric known as gatefidelity, and how close this number comes to unity reflects how well thegate maps a complete set of input states to ideal output states.

The underlying qubit architecture determines the gates that can bepractically implemented. For superconducting qubits, the single qubitgates are simple and a resolved issue; these are generated by shapedmicrowave pulses which are resonant with the frequencies correspondingto the qubit transitions and have resulted in gate fidelities betterthan 0.999. In contrast, there have been many different implementationsof the entangling two-qubit gate, each with their own set of advantagesand disadvantages. Some of these gates involve added circuit and controlcomplexity for the qubit while others place stringent requirements onthe integrity of different microwave control signals applied. To date,none of these approaches provide the same ease of control as the shapedmicrowave single qubit gates.

SUMMARY

Exemplary embodiments include a device, including a housing, at leasttwo qubits disposed in the housing and a resonator bus disposed in thehousing and coupled to the at least two qubits, wherein the at least twoqubits are maintained at a fixed frequency and are statically coupled toone another via the resonator bus, wherein energy levels |03> and |12>are closely aligned, wherein a tuned microwave signal applied to thequbit activates a two-qubit phase interaction.

Additional exemplary embodiments include a microwave-activatedcontrolled-phase gate system, including a housing, a resonator busdisposed in the housing, a first qubit disposed in the housing, a secondqubit disposed in the housing and coupled to the first qubit via theresonator bus, wherein energy levels |03> and |12> are closely aligned,wherein a tuned microwave signal is applied to the system activates atwo-qubit entangling gate.

Additional exemplary embodiments include a microwave-activatedcontrolled-phase gate system, including a housing, a resonator busdisposed in the housing, a first qubit disposed in the housing, a secondqubit disposed in the housing and coupled to the first qubit via theresonator bus, wherein the first and second qubits are transmon qubits.

Additional exemplary embodiments include a microwave-activatedcontrolled-phase gate method, including coupling a first qubit to asecond qubit via a resonator bus thereby generating amicrowave-activated controlled-phase gate, wherein a |03> energy levelis equal to a |12> energy level, tuning the microwave-activatedcontrolled-phase gate, selecting a time Tgate by sweeping through arange of durations T and establishing a two-qubit coupled system via themicrowave-activated controlled-phase gate.

Further exemplary embodiments include a microwave-activatedcontrolled-phase gate method, including coupling a first qubit to asecond qubit via a resonator bus wherein a|03> energy level is equal toa|12> energy level and applying a microwave drive signal in across-resonant manner to the first qubit, at a drive frequencyapproximately at the |1> to |2> transition of the second qubit, whereinthe microwave drive signal is split in half with a it pulse applied onthe first and second qubits inserted in between the split microwavedrive signal to remove additional phase errors.

Additional features and advantages are realized through the techniquesof the present invention. Other embodiments and aspects of the inventionare described in detail herein and are considered a part of the claimedinvention. For a better understanding of the invention with theadvantages and the features, refer to the description and to thedrawings.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

The subject matter which is regarded as the invention is particularlypointed out and distinctly claimed in the claims at the conclusion ofthe specification. The forgoing and other features, and advantages ofthe invention are apparent from the following detailed description takenin conjunction with the accompanying drawings in which:

FIG. 1 illustrates an exemplary fixed-frequency entangling two-qubitgate system;

FIG. 2 illustrates an exemplary energy level diagram;

FIG. 3 illustrates a flow chart of a method of tuning and operating anexemplary fixed-frequency entangling two-qubit gate system in accordancewith exemplary embodiments;

FIG. 4 depicts a protocol for determining a MAP gate time;

FIG. 5 depicts a slight variant of the MAP gate time of FIG. 4; and

FIG. 6 shows the data corresponding to the MAP interaction tune-up for apair of qubits.

DETAILED DESCRIPTION

In exemplary embodiments, the systems and methods described hereininclude a fixed-frequency entangling two-qubit gate between two qubits,which are statically coupled via a microwave resonator bus. FIG. 1illustrates an exemplary fixed-frequency entangling two-qubit gatesystem 100. FIG. 1 illustrates a simplified system level diagram toillustrate that numerous embodiments are contemplated. The systemincludes a housing 105 that can be any suitable superconducting ornon-superconducting material including but not limited to aluminum (Al).The system 100 further includes a resonator 110 disposed within thehousing 105. The system 100 further includes qubits 115, 120 coupled toone another, to the housing 105 and to the resonator 110. In exemplaryembodiments, the qubits can be a transmon-style superconductingJosephson junction. A transmon qubit is a superconducting qubit that ismade insensitive to charge by making the qubit capacitance large. Byadjusting the capacitance and Josephson inductance (both are determinedthrough fabrication and device geometry), the characteristic energiesassociated with the qubit capacitance (Ec) and qubit inductance (Ej)satisfy Ej>>Ec. It can be appreciated that other types of qubits arecontemplated in other exemplary embodiments. It will be appreciated thatthe qubits 115, 120 can be any suitable qubit system, including, but notlimited to: silicon-based nuclear spins, trapped ions, cavityquantum-electrodynamics, nuclear spins, electron spins in quantum dots,superconducting loops and Josephson junctions, liquid state NMR, andelectrons suspended above the surface of liquid Helium.

In exemplary embodiments, as will be appreciated further herein, thesystem 100 includes several qualities. In exemplary embodiments, thesystem 100 includes an all-microwave control of the qubits 115, 120,which can be of fixed-frequency. The system 100 has appreciable qubitseparation for high fidelity single-qubit gates and avoids leakage tohigher levels, without sacrificing two-qubit gate speeds. The system 100has the ability to function as a two-qubit phase gate. The system 100 isdrivable via any line which addresses either of the two qubits 115, 120,including the coupling resonator drive line 110. Implementing the commonresonator drive line 110 removes the need for on-chip explicit microwavedrive lines for each qubit 115, 120, simplifying the circuitconsiderably.

Conventionally, for superconducting qubits, there have been a number ofexperimentally realized two qubit gates. Their function, implementation,advantages, and disadvantages are now described. In an ISWAP gate, twotunable superconducting qubits (i.e., split-pair Cooper pair box,flux-qubit, split-pair transmon, phase qubit) are explicitly coupled viaa circuit element (capacitor, mutual inductor, common microwaveresonator). The coupling interaction is effectively turned on throughtuning the qubit energy levels via magnetic flux. In single qubitoperation mode, the two qubit ground-to-excited-state energy levels aredetuned from one another. The two qubit ISWAP gate involves dynamicallytuning the two qubits into resonance with one another for an interactiontime equal to the full swapping interaction between the two qubits. TheISWAP gate together with single qubit gates forms a universal set ofgates, from which complex quantum circuits can be derived, and generatesentangled states, such as Bell states. Advantages of the scheme are: 1)the ability to start off in a region where the qubits are very welldecoupled, permitting good single qubit control; and 2) fast turn on ofthe interaction results in gate times which can be very short, i.e.,10-100 ns. Disadvantages of the scheme are: 1) the need for tunablesuperconducting qubits which can result in reduced coherence times dueto flux noise either during the gate or in other operation regimes; 2)the presence of anharmonic energy levels of the qubit often make tuningfrequencies around difficult as it may lead to unwanted transitions orhigher level interactions; and 3) the need for on-chip fast flux biaslines with hundreds of MHz of bandwidth, which can result in additionalcircuit complexity inside the dilution refrigerator and controlelectronics.

Another conventional approach is the dynamic controlled-phase gate, inwhich two tunable superconducting qubits (i.e., split-pair transmon,capacitively-shunted flux-qubit, and phase qubit) are explicitly coupledvia a circuit element (capacitor, mutual inductor, common microwaveresonator). Similar to the dynamic ISWAP, the coupling interaction iseffectively turned on through tuning the qubit energy levels viamagnetic flux, although via a different resonance condition. In singlequbit operation mode, the two qubit ground-to-excited-state energylevels are again detuned from one another. However, this two-qubit gateinvolves dynamically tuning the energy level of the |11> state (thestate where both qubits are in their first-excited states we will usethe notation |nm> to denote n excitations in qubit 1 and m excitationsin qubit 2), into resonance with the |02> or |20> state (the stateswhere one of the qubits are in the second-excited state and the otherqubit is in the ground state). This tuning is performed again viamagnetic flux, and can be either done slowly (adiabatically), or fast,with the only constraint of picking up exactly a 180 degree phase shifton the |11> state. This technique can be calibrated and tuned up viasimple Ramsey-fringe like experiments. Advantages of the scheme are: 1)the ability to start off in a region where the qubits are very welldecoupled, permitting good single qubit control; 2) fast turn on of theinteraction results in gate times which can be very short, i.e. 10-100ns; and 3) as a two-qubit phase gate, likely residual errors aresingle-qubit phase errors, which are easily mitigated with spin-echolike sequences. Disadvantages of the scheme are: 1) the need for tunablesuperconducting qubits which can result in reduced coherence times dueto flux noise either during the gate or in other operation regimes; 2)although this gate explicitly relies on anharmonic energy levels, thepresence of other energy levels of the qubit can still make tuningfrequencies around unwieldy as it may lead to unwanted transitions orhigher level interactions; 3) the need for on-chip fast flux bias lineswith hundreds of MHz of bandwidth, which can result in additionalcircuit complexity inside the dilution refrigerator and controlelectronics; and 4) in the non-adiabatic protocol, the flux-bias must bedone very fast, but not too fast due to higher level leakage, making thecontrol difficult and in some cases impossible.

Another conventional approach is the fixed frequency sideband gate inwhich two superconducting qubits, which can be either tunable orfixed-frequency, are explicitly coupled via a common microwave quantumbus resonator. The scheme requires locating the blue sidebandtransition, corresponding to the transition between the |0, n=0>, wherethe qubit is in the ground state and there are no photons in theresonator, and the |1, n=1>, where the qubit is in the excited state and1 photon in the resonator. This transition can be driven via atwo-photon process directly on each of the qubits and must be found forboth qubits. The entangling gate, which also amounts to a combination ofthese sideband pulses into a CNOT, is performed with five sidebandpulses and several single qubit gates. Advantages of the scheme are: 1)the ability to use fixed frequency qubits, such as single junctiontransmons, or flux qubits biased to their symmetry points wherecoherence times can be optimized; and 2) all microwave control meansthat two-qubit gates can be built and controlled with the same hardwareas used for single qubit gates. Disadvantages of the scheme are: 1) theuse of transitions which involve directly populating the resonatorresults in additional decay channels during the gate; 2) for faster gatetimes (in the <100 ns range), the qubits must be pretty strongly coupledto the resonator, which can result in higher Purcell-limited relaxationrates and 3) requires on-chip explicit microwave drive lines for eachqubit, which can lead to additional crosstalk issues for differentmicrowave signals.

Another conventional approach is the fixed frequency cross resonancegate, in which two superconducting qubits (A and B), which can be eithertunable or fixed-frequency, are explicitly coupled via a circuit element(capacitor, mutual inductor, common microwave quantum bus resonator).Each qubit has its own microwave drive line. The two qubits are operatedin a regime such that there is a non-trivially small residual two-qubitdirect coupling interaction, J_eff, but separated in frequency enough topermit high-fidelity single-qubit operations. In the case of directcapacitive coupling or via a bus resonator, J_eff is largest when bothqubits are near resonant to one another, yet this arrangement can bedetrimental for performing single qubit gates. The two-qubit gate, whichgenerates a controlled-NOT gate, is performed by driving qubit A atqubit B's ground-to-excited state transition frequency. In this scheme,qubit A serves as a control and qubit B serves as the target qubit. Theinteraction can be observed by applying a single-qubit pi/2 excitationto qubit B, and turning on the cross-resonance microwave drive, with thecontrol qubit A in either its ground or excited state. The difference inoscillations from the two experiments gives the interaction strength anda half period oscillation results in a controlled-NOT gate. Advantagesof the scheme are: 1) the ability to use fixed frequency qubits, such assingle junction transmons, or flux qubits biased to their symmetrypoints where coherence times can be optimized; 2) all microwave controlmeans that two-qubit gates can be built and controlled with the samehardware as used for single qubit gates; 3) simple scalable scheme formore qubits; and 4) ability to couple non-nearest frequency neighboringqubits. Disadvantages of the scheme are: 1) gate times can be slow (˜100to 500 ns) when qubits are parked at frequency locations where highfidelity single qubit gates are also permitted; and 2) requires on-chipexplicit microwave drive lines for each qubit, which can lead toadditional crosstalk issues for different microwave signals.

In exemplary embodiments, the systems and methods described herein relyon the presence of the higher levels of the two qubits, but unlike thedynamic c-Phase gate, does not require a resonance condition betweenhigher levels and computational states (i.e., |00>, |01>, |10>, or|11>). Rather, by careful control over the design of the qubits 115, 120(i.e., controlling qubit capacitance and Josephson junction criticalcurrent), it is possible to tailor the two different qubit energy levelsto experience a resonance condition involving only higher levelnon-computational states.

FIG. 2 illustrates an exemplary energy level diagram 100 correspondingto the microwave-activated controlled phase (MAP) gate on twomulti-level superconducting qubits (e.g., in system 100 of FIG. 1),generated by having the two-qubit levels |12>, 101, and |03>, 102,aligned or close to being aligned. When the energy levels 101, 102 aredegenerate or close to degenerate, there can be an interaction 103 withstrength J. The interaction 103 serves to make the energy differences Aand B (labeled 105) different, which results in a phase gate on thetwo-qubit subspace 204 basis state |11> when a microwave tone near thefrequency of A or B transition is applied to the system 100, whichgenerates a two-qubit c-Phase gate. As such, FIG. 2 illustrates anexample design configuration that aligns the energy corresponding to|03> with the energy corresponding to |12>. Neither of these states arecomputational states for the two qubits, which means that the presenceof this fixed higher order coupling does nothing to the qubits in theidle state. However, a two qubit interaction is turned on when drivingthe system near the frequency corresponding to the transition from |01>to |02> (f_(—)12 for qubit 2), as the amount of phase picked up when thequbit is in the |11> state differs from when in any of the other statesas a result of the difference in energy between |12> and |11> beingdifferent from |02> and |01>. When the difference in phase is equal toπ, then a controlled-Phase gate has been performed. The gate is anentirely microwave-activated controlled-Phase (MAP) gate, and two-qubitinteractions are only experienced when the appropriate microwaveradiation is applied. Furthermore, this microwave-control can be appliedonto either qubit (if each qubit had a corresponding control line), orthe cavity which couples them.

The ac-stark effect is a shift of the energy levels of a system by thepresence of an external drive with amplitude Ω. The level shifts by anamount equal to the power of the external drive (Ω²) divided by thedifference in the level transition frequency (ω+δn) and the drivefrequency ω_(d). The anharmonicity of the qubit system 100 isrepresented by δ. For a superconducting qubit (or equivalent Duffingoscillator type system) the n^(th) energy level shifts according to:

$\begin{matrix}{{E_{n} = {{- \frac{( {n + 1} )\Omega^{2}}{4( {\omega + {\delta \; n} - \omega_{d}} )}} + \frac{(n)\Omega^{2}}{4( {\omega + {\delta ( {n - 1} )} - \omega_{d}} }}},} & {{EQ}.\mspace{14mu} 1}\end{matrix}$

which results in a phase shift in the qubit space of the form:

$\begin{matrix}{{\delta\varphi} = {{E_{0} - E_{1}} = {{- \; \frac{\Omega^{2}}{2( {\omega - \omega_{d}} )}} + {\frac{\Omega^{2}}{2( {\omega + \delta - \omega_{d}} )}.}}}} & {{EQ}.\mspace{14mu} 2}\end{matrix}$

From the expression, EQ. 2, this shift can be controlled by changing theeffective anharmonicity of the qubit. If this can be done conditioned onthe state of another qubit, then a conditional phase gate is achieved.In the case when the |12> level is brought into resonance with the |03>level, then the qubit frequency remains unaffected. However these twolevels have an avoided crossing and the effective anharmonicity of thesecond qubit is changed according to δ−>δ−ζ, where:

ζ=½(√{square root over (12J ²+(Δ+2δ₂)²)}−Δ−2δ₂)  EQ. 3

and Δ is the detuning between the two qubits. EQ. 3 has a maximum whenthe detuning between the qubits is equal to negative of twice theanharmonicity of the second qubit and at this operational point thedifference between the phase conditioned on the first qubit state givesthe rate of the MAP gate:

$\begin{matrix}{{\delta\varphi}_{zz} = {{{\delta\varphi}_{0} - {\delta\varphi}_{1}} \approx {- {\frac{{\zeta\Omega}^{2}}{2( {\omega + \delta - \omega_{d}} )^{2}}.}}}} & {{EQ}.\mspace{14mu} 4}\end{matrix}$

For typical values of J, EQ. 4 can have a gate time in the 100 ns-1 μsrange. It can be made faster via pulse shaping and has a fundamentallimit which for typical values can be as short as a few tens ofnanoseconds.

In exemplary embodiments, a modification to the gate can be made byapplying the drive which is at the 1 to 2 transition of the second qubitdirectly to the first qubit. This is reminiscent of the cross-resonancescheme, but still provides a conditional phase effect achieved from thedifference in the anharmonicity, but permits a reduction of directleakage out of the second qubit's energy subspace via the indirectdriving.

Another variant of the gate is to split the total gate time into twohalves, and inserting a π pulse onto both qubits in between. This pulseinsertion serves to refocus the dynamical single-qubit phases, which arepicked up by the qubits as the action of the MAP gate results in anoff-resonant ac-Stark drive from both qubits. This echoed sequence makesthe tune-up of a c-Phase unitary gate much simpler, without the need ofapplying any other additional single-qubit gates to compensate.

FIG. 3 illustrates a flowchart of a method 300 of tuning and operatingan exemplary fixed-frequency entangling two-qubit gate system (e.g., thesystem 100 of FIG. 1) in accordance with exemplary embodiments.

Although the overall microwave activated controlled-phase gate can berather general, as described above, the following is an implementationprotocol for tuning up the situation where transmon qubits have beenintentionally designed to have |03> align with |12>.

At block 310, the system 100 is established. In exemplary embodiments,the system 100 is designed such that for two transmon qubits, the |03>energy level is equal to the |12> energy level. Assuming that bothqubits are designed to have the same anharmonicity Ec, this condition isbest achieved by aiming for the |10> transition frequency to be 2 Ecdetuned from the |01> transition frequency.

At block 320, the MAP gate is tuned up by applying the pulse schemeshown in FIG. 4, which depicts a protocol 400 for determining theoptimal MAP gate time. In each of the experiments 401, and 402, thesequences are comprised of π/2 pulses applied to a second qubit,sandwiching the microwave drive at frequency w12, which should be closeto the |1> to |2> transition of the second qubit. These experimentsresult in Ramsey-fringe like patterns, with the only difference beingthat 402 gives fringes given that a first qubit is in its excited state,and experiment 401 gives fringes given that the first qubit is in itsground state. The state of the first qubit between the two experiments401, 402 is set either by doing nothing, or applying a π pulse. The timeof the MAP pulse, t is varied, and an optimal gate time Tgate isdetermined for a specific drive strength A and at a specific microwavefrequency w12, by when the fringes between the two experiments 401, 402are exactly 180 degrees out of phase. Note that in this sequence ofgates, the MAP gate can be applied directly to any of the qubits or on acommon bus resonator drive.

In exemplary embodiments, with the first qubit in either its groundstate |00> or excited state |10>, a 90 degree (π/2) pulse is firstapplied on the second qubit, followed by a microwave-tone at a frequencyf near the f_(—)12 for the second qubit, with amplitude A and durationT, and then post-pended by another 90 degree pulse on the second qubit.By choosing an f and A, and sweeping through a range of durations T, afringing pattern (Ramsey-like experiment) will be observed, which willbe different depending on the initial state of the first qubit. Thepoint of T at which the fringes are exactly π out of phase correspondsto the MAP gate time Tgate.

Referring again to FIG. 3, at block 330, the Tgate is obtained fordifferent f and A and optimized for shortness of duration and contrastof fringing pattern, giving f0 and A0.

At block 340, any two-qubit state is obtained. In exemplary embodiments,given f0, A0, and Tgate defines the MAP gate, which can now be used inconjunction with single-qubit gates on both qubits to make any two-qubitstate.

FIG. 5 depicts a slight variant of the gate, in which the MAP gate (nearresonant with |1> to |2> of qubit 2) is actually split into two sections501 and interrupted by pi pulses applied to both qubits 502, and is alsoapplied in a cross-resonant fashion, onto the first qubit. The π pulsesbetween the two halves of the MAP gate serve to refocus and residualsingle-qubit Z gates on either qubit. These echo-like sequences maketune-up of the c-Phase gate less complicated.

FIG. 6 shows the data corresponding to the MAP interaction tune-up for apair of qubits, which experience an interaction between the |12> and|03> energy levels. 601 and 602 show the result of applying the pulsesequence of FIG. 5, while varying the frequency w12 and length of theMAP gate. Fringes are observed in both cases, with level 601 being thecase with qubit 1 starting in its excited state, and level 602 being thecase with the first qubit starting in its ground state. A slice throughat the frequency 5.43 GHz gives the traces shown in 603, where a gatetime can be found at 517 ns.

The terminology used herein is for the purpose of describing particularembodiments only and is not intended to be limiting of the invention. Asused herein, the singular forms “a”, “an” and “the” are intended toinclude the plural forms as well, unless the context clearly indicatesotherwise. It will be further understood that the terms “comprises”and/or “comprising,” when used in this specification, specify thepresence of stated features, integers, steps, operations, elements,and/or components, but do not preclude the presence or addition of onemore other features, integers, steps, operations, element components,and/or groups thereof.

The corresponding structures, materials, acts, and equivalents of allmeans or step plus function elements in the claims below are intended toinclude any structure, material, or act for performing the function incombination with other claimed elements as specifically claimed. Thedescription of the present invention has been presented for purposes ofillustration and description, but is not intended to be exhaustive orlimited to the invention in the form disclosed. Many modifications andvariations will be apparent to those of ordinary skill in the artwithout departing from the scope and spirit of the invention. Theembodiment was chosen and described in order to best explain theprinciples of the invention and the practical application, and to enableothers of ordinary skill in the art to understand the invention forvarious embodiments with various modifications as are suited to theparticular use contemplated

The flow diagrams depicted herein are just one example. There may bemany variations to this diagram or the steps (or operations) describedtherein without departing from the spirit of the invention. Forinstance, the steps may be performed in a differing order or steps maybe added, deleted or modified. All of these variations are considered apart of the claimed invention.

While the preferred embodiment to the invention had been described, itwill be understood that those skilled in the art, both now and in thefuture, may make various improvements and enhancements which fall withinthe scope of the claims which follow. These claims should be construedto maintain the proper protection for the invention first described.

What is claimed is:
 1. A device, comprising: a housing; at least twoqubits disposed in the housing; and a resonator disposed in the housingand coupled to the at least two qubits, wherein the at least two qubitsare maintained at a fixed frequency and are statically coupled to oneanother via the resonator, wherein energy levels |03> and |12> areclosely aligned, wherein a tuned microwave signal applied to the qubitactivates a two-qubit phase interaction.
 2. The device as claimed inclaim 1 wherein the at least two qubits are controlled via microwavesfrom the resonator.
 3. The device as claimed in claim 1 wherein thetuned microwave signal corresponds to a frequency difference of energylevels |01> and |02>.
 4. The device as claimed in claim 1 wherein the atleast two qubits interact via a microwave-activated controlled-Phase(MAP) gate.
 5. The device as claimed in claim 4 wherein a microwaveactivated phase is generated when a two-qubit |11> state differs from asum of |01> and |10> states due to the tuned microwave signal
 6. Thedevice as claimed in claim 5 wherein the energy difference between |12>and |11>, differs from |02> and |01> when the tuned microwave signal isapplied
 7. The device as claimed in claim 6 wherein in response to adifference in phase being equal to π, a controlled-phase gate isperformed.
 8. The device as claimed in claim 1 wherein each of the atleast two qubits is a transmon qubit.
 9. A microwave-activatedcontrolled-phase (MAP) gate system, comprising: a housing; a resonatordisposed in the housing; a first qubit disposed in the housing; and asecond qubit disposed in the housing and coupled to the first qubit viathe resonator, wherein energy levels |03> and |12> are closely aligned;wherein a tuned microwave signal is applied to the qubit activates atwo-qubit phase interaction
 10. The system as claimed in claim 9 whereinthe coupling between the at least two qubits is activated by a microwavedrive at a transition frequency.
 11. The system as claimed in claim 10wherein the applied microwave drive frequency corresponds to atransition from |01> to |02>.
 12. A microwave-activated controlled-phase(MAP) gate system, comprising: a housing; a resonator disposed in thehousing; a first qubit disposed in the housing; and a second qubitdisposed in the housing and coupled to the first qubit via the resonatordrive line, wherein the first and second qubits are transmon qubits. 13.The system as claimed in claim 12 wherein a |03> energy level is equalto a |12> energy level.
 14. The system as claimed in claim 13 whereinthe first qubit is in at least one of a ground state |00> and excitedstate |10>.
 15. The system as claimed in claim 14 wherein a π/2microwave pulse is applied to the second qubit followed by a microwavedrive at the frequency corresponding to a transition from |01> to |02>.16. The system as claimed in claim 15 wherein in response to themicrowave drive applied, when a difference in phase on the second qubitbeing equal to it between when the first qubit is in |00> or |10>, acontrolled-phase gate is performed.
 17. A microwave-activatedcontrolled-phase (MAP) gate method, comprising: coupling a first qubitto a second qubit via a resonator line bus thereby generating a MAPgate, wherein a |03> energy level is equal to a|12> energy level; tuningthe MAP gate; selecting a time Tgate by sweeping through a range ofdurations T; and establishing a two-qubit coupled system via the MAPgate.
 18. The method as claimed in claim 17 wherein tuning the MAP gatecomprises applying π/2 pulses to the second qubit,
 19. The method asclaimed in claim 18 wherein the n/2 pulses establish a drive frequencyapproximately at a |1> to |2> transition of the second qubit.
 20. Themethod as claimed in claim 17 wherein the first qubit is in at least oneof a ground state |00> and an excited state |10>.
 21. The method asclaimed in claim 20 further comprising applying a π/2 microwave pulse tothe second qubit.
 22. A microwave-activated controlled-phase (MAP) gatemethod, comprising: coupling a first qubit to a second qubit via aresonator line bus wherein a |03> energy level is equal to a |12> energylevel; and applying a microwave drive signal in a cross-resonant mannerto the first qubit, at a drive frequency approximately at the |1> to |2>transition of the second qubit, wherein the microwave drive signal issplit in half with a π pulse applied on the first and second qubitsinserted in between the split microwave drive signal to removeadditional phase errors.
 23. The method as claimed in claim 22 furthercomprising tuning the MAP gate by sweeping through a range of durationsT.
 24. The method as claimed in claim 23 wherein a two-qubitcontrolled-phase gate is achieved when a π-phase shift is incurred bythe second qubit due to a MAP protocol.